LMFDB - Embedded newform 182.2.g.d.29.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [182,2,Mod(29,182)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(182, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("182.29"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	182.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,2,-1,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			29.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	182.29
Dual form			182.2.g.d.113.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 + 1.73205i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} -2.00000 q^{12} +(-3.50000 + 0.866025i) q^{13} +1.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} -1.00000 q^{18} +(2.00000 - 3.46410i) q^{19} +(-0.500000 + 0.866025i) q^{20} +2.00000 q^{21} +(1.00000 - 1.73205i) q^{22} +(-1.00000 - 1.73205i) q^{23} +(-1.00000 - 1.73205i) q^{24} -4.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} +4.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(2.50000 + 4.33013i) q^{29} +(-1.00000 + 1.73205i) q^{30} +6.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} -1.00000 q^{34} +(0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +4.00000 q^{38} +(-5.00000 - 5.19615i) q^{39} -1.00000 q^{40} +(3.50000 + 6.06218i) q^{41} +(1.00000 + 1.73205i) q^{42} +(1.00000 - 1.73205i) q^{43} +2.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(1.00000 - 1.73205i) q^{46} +(1.00000 - 1.73205i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} -2.00000 q^{51} +(1.00000 - 3.46410i) q^{52} -9.00000 q^{53} +(2.00000 + 3.46410i) q^{54} +(-1.00000 - 1.73205i) q^{55} +(-0.500000 + 0.866025i) q^{56} +8.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(3.00000 - 5.19615i) q^{59} -2.00000 q^{60} +(-2.50000 + 4.33013i) q^{61} +(3.00000 + 5.19615i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(-3.50000 + 0.866025i) q^{65} +4.00000 q^{66} +(-5.00000 - 8.66025i) q^{67} +(-0.500000 - 0.866025i) q^{68} +(2.00000 - 3.46410i) q^{69} +1.00000 q^{70} +(-8.00000 + 13.8564i) q^{71} +(0.500000 - 0.866025i) q^{72} -3.00000 q^{73} +(3.50000 - 6.06218i) q^{74} +(-4.00000 - 6.92820i) q^{75} +(2.00000 + 3.46410i) q^{76} -2.00000 q^{77} +(2.00000 - 6.92820i) q^{78} -10.0000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-3.50000 + 6.06218i) q^{82} +14.0000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(-0.500000 + 0.866025i) q^{85} +2.00000 q^{86} +(-5.00000 + 8.66025i) q^{87} +(1.00000 + 1.73205i) q^{88} +(3.00000 + 5.19615i) q^{89} -1.00000 q^{90} +(-1.00000 + 3.46410i) q^{91} +2.00000 q^{92} +(6.00000 + 10.3923i) q^{93} +(2.00000 - 3.46410i) q^{95} +2.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(0.500000 - 0.866025i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9} + q^{10} - 2 q^{11} - 4 q^{12} - 7 q^{13} + 2 q^{14} + 2 q^{15} - q^{16} - q^{17} - 2 q^{18} + 4 q^{19} - q^{20} + 4 q^{21}+ \cdots + 4 q^{99}+O(q^{100}) $ 2 * q + q^2 + 2 * q^3 - q^4 + 2 * q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9 + q^10 - 2 * q^11 - 4 * q^12 - 7 * q^13 + 2 * q^14 + 2 * q^15 - q^16 - q^17 - 2 * q^18 + 4 * q^19 - q^20 + 4 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 - 8 * q^25 - 5 * q^26 + 8 * q^27 + q^28 + 5 * q^29 - 2 * q^30 + 12 * q^31 + q^32 + 4 * q^33 - 2 * q^34 + q^35 - q^36 - 7 * q^37 + 8 * q^38 - 10 * q^39 - 2 * q^40 + 7 * q^41 + 2 * q^42 + 2 * q^43 + 4 * q^44 - q^45 + 2 * q^46 + 2 * q^48 - q^49 - 4 * q^50 - 4 * q^51 + 2 * q^52 - 18 * q^53 + 4 * q^54 - 2 * q^55 - q^56 + 16 * q^57 - 5 * q^58 + 6 * q^59 - 4 * q^60 - 5 * q^61 + 6 * q^62 + q^63 + 2 * q^64 - 7 * q^65 + 8 * q^66 - 10 * q^67 - q^68 + 4 * q^69 + 2 * q^70 - 16 * q^71 + q^72 - 6 * q^73 + 7 * q^74 - 8 * q^75 + 4 * q^76 - 4 * q^77 + 4 * q^78 - 20 * q^79 - q^80 + 11 * q^81 - 7 * q^82 + 28 * q^83 - 2 * q^84 - q^85 + 4 * q^86 - 10 * q^87 + 2 * q^88 + 6 * q^89 - 2 * q^90 - 2 * q^91 + 4 * q^92 + 12 * q^93 + 4 * q^95 + 4 * q^96 - 2 * q^97 + q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	0.995782	+	0.0917517i	$0.0292466\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	−0.418432	+	0.908248i	$0.637420\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	−1.00000	+	1.73205i	−0.408248	+	0.707107i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	−2.00000			−0.577350
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$	1.00000			0.267261
$15$	1.00000	+	1.73205i	0.258199	+	0.447214i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$	−1.00000			−0.235702
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	2.00000			0.436436
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$	−1.00000	−	1.73205i	−0.204124	−	0.353553i
$25$	−4.00000			−0.800000
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$	4.00000			0.769800
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$	−1.00000			−0.171499
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	4.00000			0.648886
$39$	−5.00000	−	5.19615i	−0.800641	−	0.832050i
$40$	−1.00000			−0.158114
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	0.998504	+	0.0546823i	$0.0174146\pi$
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	−0.451896	+	0.892071i	$0.649252\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	−0.779647	−	0.626219i	$-0.784601\pi$
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	0.932145	+	0.362084i	$0.117935\pi$
$44$	2.00000			0.301511
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	1.00000	−	1.73205i	0.147442	−	0.255377i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	1.00000	−	1.73205i	0.144338	−	0.250000i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	−2.00000			−0.280056
$52$	1.00000	−	3.46410i	0.138675	−	0.480384i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	−1.00000	−	1.73205i	−0.134840	−	0.233550i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	8.00000			1.05963
$58$	−2.50000	+	4.33013i	−0.328266	+	0.568574i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$	−2.00000			−0.258199
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$	3.00000	+	5.19615i	0.381000	+	0.659912i
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	−3.50000	+	0.866025i	−0.434122	+	0.107417i
$66$	4.00000			0.492366
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$	2.00000	−	3.46410i	0.240772	−	0.417029i
$70$	1.00000			0.119523
$71$	−8.00000	+	13.8564i	−0.949425	+	1.64445i	−0.202787	+	0.979223i	$0.565000\pi$
$71$	−8.00000	+	13.8564i	−0.949425	+	1.64445i	−0.746639	+	0.665230i	$0.768333\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−3.00000			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$73$	−3.00000			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$74$	3.50000	−	6.06218i	0.406867	−	0.704714i
$75$	−4.00000	−	6.92820i	−0.461880	−	0.800000i
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	−2.00000			−0.227921
$78$	2.00000	−	6.92820i	0.226455	−	0.784465i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	−3.50000	+	6.06218i	−0.386510	+	0.669456i
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$	−0.500000	+	0.866025i	−0.0542326	+	0.0939336i
$86$	2.00000			0.215666
$87$	−5.00000	+	8.66025i	−0.536056	+	0.928477i
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	−1.00000			−0.105409
$91$	−1.00000	+	3.46410i	−0.104828	+	0.363137i
$92$	2.00000			0.208514
$93$	6.00000	+	10.3923i	0.622171	+	1.07763i
$94$		0			0
$95$	2.00000	−	3.46410i	0.205196	−	0.355409i
$96$	2.00000			0.204124
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	2.00000			0.201008
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	−20.0000			−1.97066			−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−20.0000			−1.97066			−0.985329	+	0.170664i	$0.945409\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$	2.00000			0.195180
$106$	−4.50000	−	7.79423i	−0.437079	−	0.757042i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$	7.00000	−	12.1244i	0.664411	−	1.15079i
$112$	−1.00000			−0.0944911
$113$	−9.50000	+	16.4545i	−0.893685	+	1.54791i	−0.0582609	+	0.998301i	$0.518556\pi$
$113$	−9.50000	+	16.4545i	−0.893685	+	1.54791i	−0.835424	+	0.549606i	$0.814778\pi$
$114$	4.00000	+	6.92820i	0.374634	+	0.648886i
$115$	−1.00000	−	1.73205i	−0.0932505	−	0.161515i
$116$	−5.00000			−0.464238
$117$	1.00000	−	3.46410i	0.0924500	−	0.320256i
$118$	6.00000			0.552345
$119$	0.500000	+	0.866025i	0.0458349	+	0.0793884i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−5.00000			−0.452679
$123$	−7.00000	+	12.1244i	−0.631169	+	1.09322i
$124$	−3.00000	+	5.19615i	−0.269408	+	0.466628i
$125$	−9.00000			−0.804984
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	0.763542	−	0.645758i	$-0.223458\pi$
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	−0.941014	+	0.338368i	$0.890125\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	4.00000			0.352180
$130$	−2.50000	−	2.59808i	−0.219265	−	0.227866i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	2.00000	+	3.46410i	0.174078	+	0.301511i
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	5.00000	−	8.66025i	0.431934	−	0.748132i
$135$	4.00000			0.344265
$136$	0.500000	−	0.866025i	0.0428746	−	0.0742611i
$137$	2.50000	−	4.33013i	0.213589	−	0.369948i	−0.739246	−	0.673436i	$-0.764818\pi$
$137$	2.50000	−	4.33013i	0.213589	−	0.369948i	0.952835	+	0.303488i	$0.0981512\pi$
$138$	4.00000			0.340503
$139$	7.00000	−	12.1244i	0.593732	−	1.02837i	−0.399992	−	0.916519i	$-0.630987\pi$
$139$	7.00000	−	12.1244i	0.593732	−	1.02837i	0.993724	−	0.111856i	$-0.0356795\pi$
$140$	0.500000	+	0.866025i	0.0422577	+	0.0731925i
$141$		0			0
$142$	−16.0000			−1.34269
$143$	5.00000	+	5.19615i	0.418121	+	0.434524i
$144$	1.00000			0.0833333
$145$	2.50000	+	4.33013i	0.207614	+	0.359597i
$146$	−1.50000	−	2.59808i	−0.124141	−	0.215018i
$147$	1.00000	−	1.73205i	0.0824786	−	0.142857i
$148$	7.00000			0.575396
$149$	10.5000	−	18.1865i	0.860194	−	1.48990i	−0.0115483	−	0.999933i	$-0.503676\pi$
$149$	10.5000	−	18.1865i	0.860194	−	1.48990i	0.871742	−	0.489966i	$-0.162991\pi$
$150$	4.00000	−	6.92820i	0.326599	−	0.565685i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−2.00000	+	3.46410i	−0.162221	+	0.280976i
$153$	−0.500000	−	0.866025i	−0.0404226	−	0.0700140i
$154$	−1.00000	−	1.73205i	−0.0805823	−	0.139573i
$155$	6.00000			0.481932
$156$	7.00000	−	1.73205i	0.560449	−	0.138675i
$157$	−11.0000			−0.877896			−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−11.0000			−0.877896			−0.438948	+	0.898513i	$0.644649\pi$
$158$	−5.00000	−	8.66025i	−0.397779	−	0.688973i
$159$	−9.00000	−	15.5885i	−0.713746	−	1.23625i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−2.00000			−0.157622
$162$	−5.50000	+	9.52628i	−0.432121	+	0.748455i
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	−0.724288	−	0.689497i	$-0.757831\pi$
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	0.959266	+	0.282503i	$0.0911648\pi$
$164$	−7.00000			−0.546608
$165$	2.00000	−	3.46410i	0.155700	−	0.269680i
$166$	7.00000	+	12.1244i	0.543305	+	0.941033i
$167$	3.00000	+	5.19615i	0.232147	+	0.402090i	0.958440	−	0.285295i	$-0.0920916\pi$
$167$	3.00000	+	5.19615i	0.232147	+	0.402090i	−0.726293	+	0.687386i	$0.758758\pi$
$168$	−2.00000			−0.154303
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	−1.00000			−0.0766965
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	−0.610939	−	0.791677i	$-0.709208\pi$
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	0.991082	+	0.133250i	$0.0425415\pi$
$174$	−10.0000			−0.758098
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	12.0000			0.901975
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−23.0000			−1.70958			−0.854788	−	0.518977i	$-0.826313\pi$
$181$	−23.0000			−1.70958			−0.854788	+	0.518977i	$0.826313\pi$
$182$	−3.50000	+	0.866025i	−0.259437	+	0.0641941i
$183$	−10.0000			−0.739221
$184$	1.00000	+	1.73205i	0.0737210	+	0.127688i
$185$	−3.50000	−	6.06218i	−0.257325	−	0.445700i
$186$	−6.00000	+	10.3923i	−0.439941	+	0.762001i
$187$	2.00000			0.146254
$188$		0			0
$189$	2.00000	−	3.46410i	0.145479	−	0.251976i
$190$	4.00000			0.290191
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	1.00000	+	1.73205i	0.0721688	+	0.125000i
$193$	12.5000	+	21.6506i	0.899770	+	1.55845i	0.827788	+	0.561041i	$0.189599\pi$
$193$	12.5000	+	21.6506i	0.899770	+	1.55845i	0.0719816	+	0.997406i	$0.477068\pi$
$194$	−2.00000			−0.143592
$195$	−5.00000	−	5.19615i	−0.358057	−	0.372104i
$196$	1.00000			0.0714286
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	−0.985160	−	0.171639i	$-0.945094\pi$
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	0.343937	−	0.938993i	$-0.388239\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	4.00000			0.282843
$201$	10.0000	−	17.3205i	0.705346	−	1.22169i
$202$	−7.50000	+	12.9904i	−0.527698	+	0.914000i
$203$	5.00000			0.350931
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$	3.50000	+	6.06218i	0.244451	+	0.423401i
$206$	−10.0000	−	17.3205i	−0.696733	−	1.20678i
$207$	2.00000			0.139010
$208$	2.50000	+	2.59808i	0.173344	+	0.180144i
$209$	−8.00000			−0.553372
$210$	1.00000	+	1.73205i	0.0690066	+	0.119523i
$211$	7.00000	+	12.1244i	0.481900	+	0.834675i	0.999784	−	0.0207756i	$-0.00661356\pi$
$211$	7.00000	+	12.1244i	0.481900	+	0.834675i	−0.517884	+	0.855451i	$0.673280\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$	−32.0000			−2.19260
$214$		0			0
$215$	1.00000	−	1.73205i	0.0681994	−	0.118125i
$216$	−4.00000			−0.272166
$217$	3.00000	−	5.19615i	0.203653	−	0.352738i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	−3.00000	−	5.19615i	−0.202721	−	0.351123i
$220$	2.00000			0.134840
$221$	1.00000	−	3.46410i	0.0672673	−	0.233021i
$222$	14.0000			0.939618
$223$	6.00000	+	10.3923i	0.401790	+	0.695920i	0.993942	−	0.109906i	$-0.0350549\pi$
$223$	6.00000	+	10.3923i	0.401790	+	0.695920i	−0.592152	+	0.805826i	$0.701722\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$	−19.0000			−1.26386
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	−0.982877	−	0.184263i	$-0.941010\pi$
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	0.651015	+	0.759065i	$0.274343\pi$
$228$	−4.00000	+	6.92820i	−0.264906	+	0.458831i
$229$	−2.00000			−0.132164			−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000			−0.132164			−0.0660819	+	0.997814i	$0.521050\pi$
$230$	1.00000	−	1.73205i	0.0659380	−	0.114208i
$231$	−2.00000	−	3.46410i	−0.131590	−	0.227921i
$232$	−2.50000	−	4.33013i	−0.164133	−	0.284287i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	−10.0000	−	17.3205i	−0.649570	−	1.12509i
$238$	−0.500000	+	0.866025i	−0.0324102	+	0.0561361i
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$	1.00000	−	1.73205i	0.0645497	−	0.111803i
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	−0.378963	−	0.925412i	$-0.623719\pi$
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	0.990912	−	0.134515i	$-0.0429475\pi$
$242$	7.00000			0.449977
$243$	−5.00000	+	8.66025i	−0.320750	+	0.555556i
$244$	−2.50000	−	4.33013i	−0.160046	−	0.277208i
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$	−14.0000			−0.892607
$247$	−4.00000	+	13.8564i	−0.254514	+	0.881662i
$248$	−6.00000			−0.381000
$249$	14.0000	+	24.2487i	0.887214	+	1.53670i
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	−10.0000	+	17.3205i	−0.631194	+	1.09326i	0.356113	+	0.934443i	$0.384102\pi$
$251$	−10.0000	+	17.3205i	−0.631194	+	1.09326i	−0.987308	+	0.158818i	$0.949232\pi$
$252$	−1.00000			−0.0629941
$253$	−2.00000	+	3.46410i	−0.125739	+	0.217786i
$254$	2.00000	−	3.46410i	0.125491	−	0.217357i
$255$	−2.00000			−0.125245
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$	2.00000	+	3.46410i	0.124515	+	0.215666i
$259$	−7.00000			−0.434959
$260$	1.00000	−	3.46410i	0.0620174	−	0.214834i
$261$	−5.00000			−0.309492
$262$		0			0
$263$	7.00000	+	12.1244i	0.431638	+	0.747620i	0.997015	−	0.0772134i	$-0.0246023\pi$
$263$	7.00000	+	12.1244i	0.431638	+	0.747620i	−0.565376	+	0.824833i	$0.691269\pi$
$264$	−2.00000	+	3.46410i	−0.123091	+	0.213201i
$265$	−9.00000			−0.552866
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	−6.00000	+	10.3923i	−0.367194	+	0.635999i
$268$	10.0000			0.610847
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	2.00000	+	3.46410i	0.121716	+	0.210819i
$271$	15.0000	+	25.9808i	0.911185	+	1.57822i	0.812393	+	0.583111i	$0.198165\pi$
$271$	15.0000	+	25.9808i	0.911185	+	1.57822i	0.0987925	+	0.995108i	$0.468502\pi$
$272$	1.00000			0.0606339
$273$	−7.00000	+	1.73205i	−0.423659	+	0.104828i
$274$	5.00000			0.302061
$275$	4.00000	+	6.92820i	0.241209	+	0.417786i
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	−0.489207	−	0.872167i	$-0.662714\pi$
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	0.999923	−	0.0124177i	$-0.00395278\pi$
$278$	14.0000			0.839664
$279$	−3.00000	+	5.19615i	−0.179605	+	0.311086i
$280$	−0.500000	+	0.866025i	−0.0298807	+	0.0517549i
$281$	−29.0000			−1.72999			−0.864997	−	0.501776i	$-0.832680\pi$
$281$	−29.0000			−1.72999			−0.864997	+	0.501776i	$0.832680\pi$
$282$		0			0
$283$	11.0000	+	19.0526i	0.653882	+	1.13256i	0.982173	+	0.187980i	$0.0601941\pi$
$283$	11.0000	+	19.0526i	0.653882	+	1.13256i	−0.328291	+	0.944577i	$0.606473\pi$
$284$	−8.00000	−	13.8564i	−0.474713	−	0.822226i
$285$	8.00000			0.473879
$286$	−2.00000	+	6.92820i	−0.118262	+	0.409673i
$287$	7.00000			0.413197
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$	−2.50000	+	4.33013i	−0.146805	+	0.254274i
$291$	−4.00000			−0.234484
$292$	1.50000	−	2.59808i	0.0877809	−	0.152041i
$293$	3.50000	−	6.06218i	0.204472	−	0.354156i	−0.745492	−	0.666514i	$-0.767786\pi$
$293$	3.50000	−	6.06218i	0.204472	−	0.354156i	0.949964	+	0.312358i	$0.101119\pi$
$294$	2.00000			0.116642
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$	3.50000	+	6.06218i	0.203433	+	0.352357i
$297$	−4.00000	−	6.92820i	−0.232104	−	0.402015i
$298$	21.0000			1.21650
$299$	5.00000	+	5.19615i	0.289157	+	0.300501i
$300$	8.00000			0.461880
$301$	−1.00000	−	1.73205i	−0.0576390	−	0.0998337i
$302$	4.00000	+	6.92820i	0.230174	+	0.398673i
$303$	−15.0000	+	25.9808i	−0.861727	+	1.49256i
$304$	−4.00000			−0.229416
$305$	−2.50000	+	4.33013i	−0.143150	+	0.247942i
$306$	0.500000	−	0.866025i	0.0285831	−	0.0495074i
$307$	−6.00000			−0.342438			−0.171219	−	0.985233i	$-0.554771\pi$
$307$	−6.00000			−0.342438			−0.171219	+	0.985233i	$0.554771\pi$
$308$	1.00000	−	1.73205i	0.0569803	−	0.0986928i
$309$	−20.0000	−	34.6410i	−1.13776	−	1.97066i
$310$	3.00000	+	5.19615i	0.170389	+	0.295122i
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$	5.00000	+	5.19615i	0.283069	+	0.294174i
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	−5.50000	−	9.52628i	−0.310383	−	0.537599i
$315$	0.500000	+	0.866025i	0.0281718	+	0.0487950i
$316$	5.00000	−	8.66025i	0.281272	−	0.487177i
$317$	−25.0000			−1.40414			−0.702070	−	0.712108i	$-0.747741\pi$
$317$	−25.0000			−1.40414			−0.702070	+	0.712108i	$0.747741\pi$
$318$	9.00000	−	15.5885i	0.504695	−	0.874157i
$319$	5.00000	−	8.66025i	0.279946	−	0.484881i
$320$	1.00000			0.0559017
$321$		0			0
$322$	−1.00000	−	1.73205i	−0.0557278	−	0.0965234i
$323$	2.00000	+	3.46410i	0.111283	+	0.192748i
$324$	−11.0000			−0.611111
$325$	14.0000	−	3.46410i	0.776580	−	0.192154i
$326$	6.00000			0.332309
$327$	2.00000	+	3.46410i	0.110600	+	0.191565i
$328$	−3.50000	−	6.06218i	−0.193255	−	0.334728i
$329$		0			0
$330$	4.00000			0.220193
$331$	9.00000	−	15.5885i	0.494685	−	0.856819i	−0.505296	−	0.862946i	$-0.668617\pi$
$331$	9.00000	−	15.5885i	0.494685	−	0.856819i	0.999981	+	0.00612670i	$0.00195020\pi$
$332$	−7.00000	+	12.1244i	−0.384175	+	0.665410i
$333$	7.00000			0.383598
$334$	−3.00000	+	5.19615i	−0.164153	+	0.284321i
$335$	−5.00000	−	8.66025i	−0.273179	−	0.473160i
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$	27.0000			1.47078			0.735392	−	0.677642i	$-0.236998\pi$
$337$	27.0000			1.47078			0.735392	+	0.677642i	$0.236998\pi$
$338$	11.0000	+	6.92820i	0.598321	+	0.376845i
$339$	−38.0000			−2.06388
$340$	−0.500000	−	0.866025i	−0.0271163	−	0.0469668i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	−2.00000	+	3.46410i	−0.108148	+	0.187317i
$343$	−1.00000			−0.0539949
$344$	−1.00000	+	1.73205i	−0.0539164	+	0.0933859i
$345$	2.00000	−	3.46410i	0.107676	−	0.186501i
$346$	10.0000			0.537603
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	−0.614664	−	0.788789i	$-0.710708\pi$
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	0.990443	+	0.137920i	$0.0440416\pi$
$348$	−5.00000	−	8.66025i	−0.268028	−	0.464238i
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	0.838019	−	0.545640i	$-0.183714\pi$
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	−0.891548	+	0.452926i	$0.850380\pi$
$350$	−4.00000			−0.213809
$351$	−14.0000	+	3.46410i	−0.747265	+	0.184900i
$352$	−2.00000			−0.106600
$353$	−12.5000	−	21.6506i	−0.665308	−	1.15235i	−0.979202	−	0.202889i	$-0.934967\pi$
$353$	−12.5000	−	21.6506i	−0.665308	−	1.15235i	0.313894	−	0.949458i	$-0.398366\pi$
$354$	6.00000	+	10.3923i	0.318896	+	0.552345i
$355$	−8.00000	+	13.8564i	−0.424596	+	0.735422i
$356$	−6.00000			−0.317999
$357$	−1.00000	+	1.73205i	−0.0529256	+	0.0916698i
$358$		0			0
$359$	−36.0000			−1.90001			−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000			−1.90001			−0.950004	+	0.312239i	$0.898921\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	−11.5000	−	19.9186i	−0.604427	−	1.04690i
$363$	14.0000			0.734809
$364$	−2.50000	−	2.59808i	−0.131036	−	0.136176i
$365$	−3.00000			−0.157027
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	−3.00000	−	5.19615i	−0.156599	−	0.271237i	0.777041	−	0.629450i	$-0.216720\pi$
$367$	−3.00000	−	5.19615i	−0.156599	−	0.271237i	−0.933640	+	0.358213i	$0.883386\pi$
$368$	−1.00000	+	1.73205i	−0.0521286	+	0.0902894i
$369$	−7.00000			−0.364405
$370$	3.50000	−	6.06218i	0.181956	−	0.315158i
$371$	−4.50000	+	7.79423i	−0.233628	+	0.404656i
$372$	−12.0000			−0.622171
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	−0.999956	−	0.00933789i	$-0.997028\pi$
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	0.508065	+	0.861319i	$0.330361\pi$
$374$	1.00000	+	1.73205i	0.0517088	+	0.0895622i
$375$	−9.00000	−	15.5885i	−0.464758	−	0.804984i
$376$		0			0
$377$	−12.5000	−	12.9904i	−0.643783	−	0.669039i
$378$	4.00000			0.205738
$379$	−17.0000	−	29.4449i	−0.873231	−	1.51248i	−0.858635	−	0.512588i	$-0.828687\pi$
$379$	−17.0000	−	29.4449i	−0.873231	−	1.51248i	−0.0145964	−	0.999893i	$-0.504646\pi$
$380$	2.00000	+	3.46410i	0.102598	+	0.177705i
$381$	4.00000	−	6.92820i	0.204926	−	0.354943i
$382$	6.00000			0.306987
$383$	9.00000	−	15.5885i	0.459879	−	0.796533i	−0.539076	−	0.842257i	$-0.681226\pi$
$383$	9.00000	−	15.5885i	0.459879	−	0.796533i	0.998954	+	0.0457244i	$0.0145596\pi$
$384$	−1.00000	+	1.73205i	−0.0510310	+	0.0883883i
$385$	−2.00000			−0.101929
$386$	−12.5000	+	21.6506i	−0.636233	+	1.10199i
$387$	1.00000	+	1.73205i	0.0508329	+	0.0880451i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	23.0000			1.16615			0.583073	−	0.812420i	$-0.301850\pi$
$389$	23.0000			1.16615			0.583073	+	0.812420i	$0.301850\pi$
$390$	2.00000	−	6.92820i	0.101274	−	0.350823i
$391$	2.00000			0.101144
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	−10.0000			−0.503155
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	20.0000			1.00251
$399$	4.00000	−	6.92820i	0.200250	−	0.346844i
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−11.5000	−	19.9186i	−0.574283	−	0.994687i	−0.996119	−	0.0880147i	$-0.971948\pi$
$401$	−11.5000	−	19.9186i	−0.574283	−	0.994687i	0.421837	−	0.906672i	$-0.361386\pi$
$402$	20.0000			0.997509
$403$	−21.0000	+	5.19615i	−1.04608	+	0.258839i
$404$	−15.0000			−0.746278
$405$	5.50000	+	9.52628i	0.273297	+	0.473365i
$406$	2.50000	+	4.33013i	0.124073	+	0.214901i
$407$	−7.00000	+	12.1244i	−0.346977	+	0.600982i
$408$	2.00000			0.0990148
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	0.939490	−	0.342578i	$-0.111300\pi$
$410$	−3.50000	+	6.06218i	−0.172853	+	0.299390i
$411$	10.0000			0.493264
$412$	10.0000	−	17.3205i	0.492665	−	0.853320i
$413$	−3.00000	−	5.19615i	−0.147620	−	0.255686i
$414$	1.00000	+	1.73205i	0.0491473	+	0.0851257i
$415$	14.0000			0.687233
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	28.0000			1.37117
$418$	−4.00000	−	6.92820i	−0.195646	−	0.338869i
$419$	5.00000	+	8.66025i	0.244266	+	0.423081i	0.961925	−	0.273314i	$-0.0881197\pi$
$419$	5.00000	+	8.66025i	0.244266	+	0.423081i	−0.717659	+	0.696395i	$0.754786\pi$
$420$	−1.00000	+	1.73205i	−0.0487950	+	0.0845154i
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	−7.00000	+	12.1244i	−0.340755	+	0.590204i
$423$		0			0
$424$	9.00000			0.437079
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$	−16.0000	−	27.7128i	−0.775203	−	1.34269i
$427$	2.50000	+	4.33013i	0.120983	+	0.209550i
$428$		0			0
$429$	−4.00000	+	13.8564i	−0.193122	+	0.668994i
$430$	2.00000			0.0964486
$431$	−10.0000	−	17.3205i	−0.481683	−	0.834300i	0.518096	−	0.855323i	$-0.326641\pi$
$431$	−10.0000	−	17.3205i	−0.481683	−	0.834300i	−0.999779	+	0.0210230i	$0.993308\pi$
$432$	−2.00000	−	3.46410i	−0.0962250	−	0.166667i
$433$	−4.50000	+	7.79423i	−0.216256	+	0.374567i	−0.953660	−	0.300885i	$-0.902718\pi$
$433$	−4.50000	+	7.79423i	−0.216256	+	0.374567i	0.737404	+	0.675452i	$0.236051\pi$
$434$	6.00000			0.288009
$435$	−5.00000	+	8.66025i	−0.239732	+	0.415227i
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−8.00000			−0.382692
$438$	3.00000	−	5.19615i	0.143346	−	0.248282i
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$	1.00000	+	1.73205i	0.0476731	+	0.0825723i
$441$	1.00000			0.0476190
$442$	3.50000	−	0.866025i	0.166478	−	0.0411926i
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$	7.00000	+	12.1244i	0.332205	+	0.575396i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	−6.00000	+	10.3923i	−0.284108	+	0.492090i
$447$	42.0000			1.98653
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	0.257743	+	0.966213i	$0.417021\pi$
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	−0.965637	+	0.259895i	$0.916312\pi$
$450$	4.00000			0.188562
$451$	7.00000	−	12.1244i	0.329617	−	0.570914i
$452$	−9.50000	−	16.4545i	−0.446842	−	0.773954i
$453$	8.00000	+	13.8564i	0.375873	+	0.651031i
$454$	−10.0000			−0.469323
$455$	−1.00000	+	3.46410i	−0.0468807	+	0.162400i
$456$	−8.00000			−0.374634
$457$	4.50000	+	7.79423i	0.210501	+	0.364599i	0.951871	−	0.306497i	$-0.0991571\pi$
$457$	4.50000	+	7.79423i	0.210501	+	0.364599i	−0.741370	+	0.671096i	$0.765824\pi$
$458$	−1.00000	−	1.73205i	−0.0467269	−	0.0809334i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$	2.00000			0.0932505
$461$	5.50000	−	9.52628i	0.256161	−	0.443683i	−0.709050	−	0.705159i	$-0.750876\pi$
$461$	5.50000	−	9.52628i	0.256161	−	0.443683i	0.965210	+	0.261476i	$0.0842091\pi$
$462$	2.00000	−	3.46410i	0.0930484	−	0.161165i
$463$	18.0000			0.836531			0.418265	−	0.908325i	$-0.362638\pi$
$463$	18.0000			0.836531			0.418265	+	0.908325i	$0.362638\pi$
$464$	2.50000	−	4.33013i	0.116060	−	0.201021i
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	−2.00000			−0.0925490			−0.0462745	−	0.998929i	$-0.514735\pi$
$467$	−2.00000			−0.0925490			−0.0462745	+	0.998929i	$0.514735\pi$
$468$	2.50000	+	2.59808i	0.115563	+	0.120096i
$469$	−10.0000			−0.461757
$470$		0			0
$471$	−11.0000	−	19.0526i	−0.506853	−	0.877896i
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	−4.00000			−0.183920
$474$	10.0000	−	17.3205i	0.459315	−	0.795557i
$475$	−8.00000	+	13.8564i	−0.367065	+	0.635776i
$476$	−1.00000			−0.0458349
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$	9.00000	+	15.5885i	0.411650	+	0.712999i
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	0.926388	−	0.376571i	$-0.122897\pi$
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	−0.789314	+	0.613990i	$0.789564\pi$
$480$	2.00000			0.0912871
$481$	17.5000	+	18.1865i	0.797931	+	0.829235i
$482$	19.0000			0.865426
$483$	−2.00000	−	3.46410i	−0.0910032	−	0.157622i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	−10.0000			−0.453609
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	0.233933	+	0.972253i	$0.424840\pi$
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	−0.958962	+	0.283535i	$0.908493\pi$
$488$	2.50000	−	4.33013i	0.113170	−	0.196016i
$489$	12.0000			0.542659
$490$	0.500000	−	0.866025i	0.0225877	−	0.0391230i
$491$	−8.00000	−	13.8564i	−0.361035	−	0.625331i	0.627096	−	0.778942i	$-0.284243\pi$
$491$	−8.00000	−	13.8564i	−0.361035	−	0.625331i	−0.988131	+	0.153611i	$0.950910\pi$
$492$	−7.00000	−	12.1244i	−0.315584	−	0.546608i
$493$	−5.00000			−0.225189
$494$	−14.0000	+	3.46410i	−0.629890	+	0.155857i
$495$	2.00000			0.0898933
$496$	−3.00000	−	5.19615i	−0.134704	−	0.233314i
$497$	8.00000	+	13.8564i	0.358849	+	0.621545i
$498$	−14.0000	+	24.2487i	−0.627355	+	1.08661i
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$	−20.0000			−0.892644
$503$	−7.00000	+	12.1244i	−0.312115	+	0.540598i	−0.978820	−	0.204723i	$-0.934371\pi$
$503$	−7.00000	+	12.1244i	−0.312115	+	0.540598i	0.666705	+	0.745321i	$0.267704\pi$
$504$	−0.500000	−	0.866025i	−0.0222718	−	0.0385758i
$505$	7.50000	+	12.9904i	0.333746	+	0.578064i
$506$	−4.00000			−0.177822
$507$	22.0000	+	13.8564i	0.977054	+	0.615385i
$508$	4.00000			0.177471
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$	−1.00000	−	1.73205i	−0.0442807	−	0.0766965i
$511$	−1.50000	+	2.59808i	−0.0663561	+	0.114932i
$512$	−1.00000			−0.0441942
$513$	8.00000	−	13.8564i	0.353209	−	0.611775i
$514$	−7.50000	+	12.9904i	−0.330811	+	0.572981i
$515$	−20.0000			−0.881305
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$		0			0
$518$	−3.50000	−	6.06218i	−0.153781	−	0.266357i
$519$	20.0000			0.877903
$520$	3.50000	−	0.866025i	0.153485	−	0.0379777i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	−2.50000	−	4.33013i	−0.109422	−	0.189525i
$523$	−18.0000	−	31.1769i	−0.787085	−	1.36327i	−0.927746	−	0.373213i	$-0.878256\pi$
$523$	−18.0000	−	31.1769i	−0.787085	−	1.36327i	0.140660	−	0.990058i	$-0.455077\pi$
$524$		0			0
$525$	−8.00000			−0.349149
$526$	−7.00000	+	12.1244i	−0.305215	+	0.528647i
$527$	−3.00000	+	5.19615i	−0.130682	+	0.226348i
$528$	−4.00000			−0.174078
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$	3.00000	+	5.19615i	0.130189	+	0.225494i
$532$	4.00000			0.173422
$533$	−17.5000	−	18.1865i	−0.758009	−	0.787746i
$534$	−12.0000			−0.519291
$535$		0			0
$536$	5.00000	+	8.66025i	0.215967	+	0.374066i
$537$		0			0
$538$	−18.0000			−0.776035
$539$	−1.00000	+	1.73205i	−0.0430730	+	0.0746047i
$540$	−2.00000	+	3.46410i	−0.0860663	+	0.149071i
$541$	7.00000			0.300954			0.150477	−	0.988614i	$-0.451919\pi$
$541$	7.00000			0.300954			0.150477	+	0.988614i	$0.451919\pi$
$542$	−15.0000	+	25.9808i	−0.644305	+	1.11597i
$543$	−23.0000	−	39.8372i	−0.987024	−	1.70958i
$544$	0.500000	+	0.866025i	0.0214373	+	0.0371305i
$545$	2.00000			0.0856706
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$	38.0000			1.62476			0.812381	−	0.583127i	$-0.198171\pi$
$547$	38.0000			1.62476			0.812381	+	0.583127i	$0.198171\pi$
$548$	2.50000	+	4.33013i	0.106795	+	0.184974i
$549$	−2.50000	−	4.33013i	−0.106697	−	0.184805i
$550$	−4.00000	+	6.92820i	−0.170561	+	0.295420i
$551$	20.0000			0.852029
$552$	−2.00000	+	3.46410i	−0.0851257	+	0.147442i
$553$	−5.00000	+	8.66025i	−0.212622	+	0.368271i
$554$	17.0000			0.722261
$555$	7.00000	−	12.1244i	0.297133	−	0.514650i
$556$	7.00000	+	12.1244i	0.296866	+	0.514187i
$557$	−3.50000	−	6.06218i	−0.148300	−	0.256863i	0.782299	−	0.622903i	$-0.214047\pi$
$557$	−3.50000	−	6.06218i	−0.148300	−	0.256863i	−0.930599	+	0.366040i	$0.880713\pi$
$558$	−6.00000			−0.254000
$559$	−2.00000	+	6.92820i	−0.0845910	+	0.293032i
$560$	−1.00000			−0.0422577
$561$	2.00000	+	3.46410i	0.0844401	+	0.146254i
$562$	−14.5000	−	25.1147i	−0.611646	−	1.05940i
$563$	−7.00000	+	12.1244i	−0.295015	+	0.510981i	−0.974988	−	0.222256i	$-0.928658\pi$
$563$	−7.00000	+	12.1244i	−0.295015	+	0.510981i	0.679974	+	0.733237i	$0.261991\pi$
$564$		0			0
$565$	−9.50000	+	16.4545i	−0.399668	+	0.692245i
$566$	−11.0000	+	19.0526i	−0.462364	+	0.800839i
$567$	11.0000			0.461957
$568$	8.00000	−	13.8564i	0.335673	−	0.581402i
$569$	−7.00000	−	12.1244i	−0.293455	−	0.508279i	0.681169	−	0.732126i	$-0.261472\pi$
$569$	−7.00000	−	12.1244i	−0.293455	−	0.508279i	−0.974624	+	0.223847i	$0.928139\pi$
$570$	4.00000	+	6.92820i	0.167542	+	0.290191i
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$	−7.00000	+	1.73205i	−0.292685	+	0.0724207i
$573$	12.0000			0.501307
$574$	3.50000	+	6.06218i	0.146087	+	0.253030i
$575$	4.00000	+	6.92820i	0.166812	+	0.288926i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−39.0000			−1.62359			−0.811796	−	0.583942i	$-0.801510\pi$
$577$	−39.0000			−1.62359			−0.811796	+	0.583942i	$0.801510\pi$
$578$	−8.00000	+	13.8564i	−0.332756	+	0.576351i
$579$	−25.0000	+	43.3013i	−1.03896	+	1.79954i
$580$	−5.00000			−0.207614
$581$	7.00000	−	12.1244i	0.290409	−	0.503003i
$582$	−2.00000	−	3.46410i	−0.0829027	−	0.143592i
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$	3.00000			0.124141
$585$	1.00000	−	3.46410i	0.0413449	−	0.143223i
$586$	7.00000			0.289167
$587$	−6.00000	−	10.3923i	−0.247647	−	0.428936i	0.715226	−	0.698893i	$-0.246324\pi$
$587$	−6.00000	−	10.3923i	−0.247647	−	0.428936i	−0.962872	+	0.269957i	$0.912990\pi$
$588$	1.00000	+	1.73205i	0.0412393	+	0.0714286i
$589$	12.0000	−	20.7846i	0.494451	−	0.856415i
$590$	6.00000			0.247016
$591$	18.0000	−	31.1769i	0.740421	−	1.28245i
$592$	−3.50000	+	6.06218i	−0.143849	+	0.249154i
$593$	−19.0000			−0.780236			−0.390118	−	0.920765i	$-0.627566\pi$
$593$	−19.0000			−0.780236			−0.390118	+	0.920765i	$0.627566\pi$
$594$	4.00000	−	6.92820i	0.164122	−	0.284268i
$595$	0.500000	+	0.866025i	0.0204980	+	0.0355036i
$596$	10.5000	+	18.1865i	0.430097	+	0.744949i
$597$	40.0000			1.63709
$598$	−2.00000	+	6.92820i	−0.0817861	+	0.283315i
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$	4.00000	+	6.92820i	0.163299	+	0.282843i
$601$	15.5000	+	26.8468i	0.632258	+	1.09510i	0.987089	+	0.160173i	$0.0512051\pi$
$601$	15.5000	+	26.8468i	0.632258	+	1.09510i	−0.354831	+	0.934931i	$0.615462\pi$
$602$	1.00000	−	1.73205i	0.0407570	−	0.0705931i
$603$	10.0000			0.407231
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$	−30.0000			−1.21867
$607$	2.00000	−	3.46410i	0.0811775	−	0.140604i	−0.822578	−	0.568652i	$-0.807465\pi$
$607$	2.00000	−	3.46410i	0.0811775	−	0.140604i	0.903756	+	0.428048i	$0.140799\pi$
$608$	−2.00000	−	3.46410i	−0.0811107	−	0.140488i
$609$	5.00000	+	8.66025i	0.202610	+	0.350931i
$610$	−5.00000			−0.202444
$611$		0			0
$612$	1.00000			0.0404226
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$	−3.00000	−	5.19615i	−0.121070	−	0.209700i
$615$	−7.00000	+	12.1244i	−0.282267	+	0.488901i
$616$	2.00000			0.0805823
$617$	2.50000	−	4.33013i	0.100646	−	0.174324i	−0.811305	−	0.584623i	$-0.801242\pi$
$617$	2.50000	−	4.33013i	0.100646	−	0.174324i	0.911951	+	0.410299i	$0.134576\pi$
$618$	20.0000	−	34.6410i	0.804518	−	1.39347i
$619$	26.0000			1.04503			0.522514	−	0.852631i	$-0.324994\pi$
$619$	26.0000			1.04503			0.522514	+	0.852631i	$0.324994\pi$
$620$	−3.00000	+	5.19615i	−0.120483	+	0.208683i
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$	15.0000	+	25.9808i	0.601445	+	1.04173i
$623$	6.00000			0.240385
$624$	−2.00000	+	6.92820i	−0.0800641	+	0.277350i
$625$	11.0000			0.440000
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$	−8.00000	−	13.8564i	−0.319489	−	0.553372i
$628$	5.50000	−	9.52628i	0.219474	−	0.380140i
$629$	7.00000			0.279108
$630$	−0.500000	+	0.866025i	−0.0199205	+	0.0345033i
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	−0.595397	−	0.803432i	$-0.703005\pi$
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	0.993491	+	0.113913i	$0.0363385\pi$
$632$	10.0000			0.397779
$633$	−14.0000	+	24.2487i	−0.556450	+	0.963800i
$634$	−12.5000	−	21.6506i	−0.496438	−	0.859857i
$635$	−2.00000	−	3.46410i	−0.0793676	−	0.137469i
$636$	18.0000			0.713746
$637$	2.50000	+	2.59808i	0.0990536	+	0.102940i
$638$	10.0000			0.395904
$639$	−8.00000	−	13.8564i	−0.316475	−	0.548151i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	0.500000	−	0.866025i	0.0197488	−	0.0342059i	−0.855982	−	0.517005i	$-0.827047\pi$
$641$	0.500000	−	0.866025i	0.0197488	−	0.0342059i	0.875731	+	0.482800i	$0.160380\pi$
$642$		0			0
$643$	−4.00000	+	6.92820i	−0.157745	+	0.273222i	−0.934055	−	0.357129i	$-0.883756\pi$
$643$	−4.00000	+	6.92820i	−0.157745	+	0.273222i	0.776310	+	0.630351i	$0.217089\pi$
$644$	1.00000	−	1.73205i	0.0394055	−	0.0682524i
$645$	4.00000			0.157500
$646$	−2.00000	+	3.46410i	−0.0786889	+	0.136293i
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$	−5.50000	−	9.52628i	−0.216060	−	0.374228i
$649$	−12.0000			−0.471041
$650$	10.0000	+	10.3923i	0.392232	+	0.407620i
$651$	12.0000			0.470317
$652$	3.00000	+	5.19615i	0.117489	+	0.203497i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$	−2.00000	+	3.46410i	−0.0782062	+	0.135457i
$655$		0			0
$656$	3.50000	−	6.06218i	0.136652	−	0.236688i
$657$	1.50000	−	2.59808i	0.0585206	−	0.101361i
$658$		0			0
$659$	24.0000	−	41.5692i	0.934907	−	1.61931i	0.160108	−	0.987099i	$-0.448816\pi$
$659$	24.0000	−	41.5692i	0.934907	−	1.61931i	0.774799	−	0.632207i	$-0.217851\pi$
$660$	2.00000	+	3.46410i	0.0778499	+	0.134840i
$661$	11.5000	+	19.9186i	0.447298	+	0.774743i	0.998209	−	0.0598209i	$-0.0190530\pi$
$661$	11.5000	+	19.9186i	0.447298	+	0.774743i	−0.550911	+	0.834564i	$0.685720\pi$
$662$	18.0000			0.699590
$663$	7.00000	−	1.73205i	0.271857	−	0.0672673i
$664$	−14.0000			−0.543305
$665$	−2.00000	−	3.46410i	−0.0775567	−	0.134332i
$666$	3.50000	+	6.06218i	0.135622	+	0.234905i
$667$	5.00000	−	8.66025i	0.193601	−	0.335326i
$668$	−6.00000			−0.232147
$669$	−12.0000	+	20.7846i	−0.463947	+	0.803579i
$670$	5.00000	−	8.66025i	0.193167	−	0.334575i
$671$	10.0000			0.386046
$672$	1.00000	−	1.73205i	0.0385758	−	0.0668153i
$673$	−13.5000	−	23.3827i	−0.520387	−	0.901336i	−0.999719	−	0.0237028i	$-0.992454\pi$
$673$	−13.5000	−	23.3827i	−0.520387	−	0.901336i	0.479332	−	0.877633i	$-0.340879\pi$
$674$	13.5000	+	23.3827i	0.520001	+	0.900667i
$675$	−16.0000			−0.615840
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$	22.0000			0.845529			0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000			0.845529			0.422764	+	0.906240i	$0.361060\pi$
$678$	−19.0000	−	32.9090i	−0.729691	−	1.26386i
$679$	1.00000	+	1.73205i	0.0383765	+	0.0664700i
$680$	0.500000	−	0.866025i	0.0191741	−	0.0332106i
$681$	−20.0000			−0.766402
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	4.00000	−	6.92820i	0.153056	−	0.265100i	−0.779294	−	0.626659i	$-0.784422\pi$
$683$	4.00000	−	6.92820i	0.153056	−	0.265100i	0.932349	+	0.361559i	$0.117755\pi$
$684$	−4.00000			−0.152944
$685$	2.50000	−	4.33013i	0.0955201	−	0.165446i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	−2.00000	−	3.46410i	−0.0763048	−	0.132164i
$688$	−2.00000			−0.0762493
$689$	31.5000	−	7.79423i	1.20005	−	0.296936i
$690$	4.00000			0.152277
$691$	−20.0000	−	34.6410i	−0.760836	−	1.31781i	−0.942420	−	0.334431i	$-0.891456\pi$
$691$	−20.0000	−	34.6410i	−0.760836	−	1.31781i	0.181584	−	0.983375i	$-0.441877\pi$
$692$	5.00000	+	8.66025i	0.190071	+	0.329213i
$693$	1.00000	−	1.73205i	0.0379869	−	0.0657952i
$694$	14.0000			0.531433
$695$	7.00000	−	12.1244i	0.265525	−	0.459903i
$696$	5.00000	−	8.66025i	0.189525	−	0.328266i
$697$	−7.00000			−0.265144
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$	14.0000	+	24.2487i	0.529529	+	0.917170i
$700$	−2.00000	−	3.46410i	−0.0755929	−	0.130931i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	−10.0000	−	10.3923i	−0.377426	−	0.392232i
$703$	−28.0000			−1.05604
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$		0			0
$706$	12.5000	−	21.6506i	0.470444	−	0.814832i
$707$	15.0000			0.564133
$708$	−6.00000	+	10.3923i	−0.225494	+	0.390567i
$709$	−19.5000	+	33.7750i	−0.732338	+	1.26845i	0.223544	+	0.974694i	$0.428237\pi$
$709$	−19.5000	+	33.7750i	−0.732338	+	1.26845i	−0.955882	+	0.293752i	$0.905096\pi$
$710$	−16.0000			−0.600469
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−6.00000	−	10.3923i	−0.224702	−	0.389195i
$714$	−2.00000			−0.0748481
$715$	5.00000	+	5.19615i	0.186989	+	0.194325i
$716$		0			0
$717$	18.0000	+	31.1769i	0.672222	+	1.16432i
$718$	−18.0000	−	31.1769i	−0.671754	−	1.16351i
$719$	11.0000	−	19.0526i	0.410231	−	0.710541i	−0.584684	−	0.811261i	$-0.698781\pi$
$719$	11.0000	−	19.0526i	0.410231	−	0.710541i	0.994915	+	0.100721i	$0.0321148\pi$
$720$	1.00000			0.0372678
$721$	−10.0000	+	17.3205i	−0.372419	+	0.645049i
$722$	−1.50000	+	2.59808i	−0.0558242	+	0.0966904i
$723$	38.0000			1.41324
$724$	11.5000	−	19.9186i	0.427394	−	0.740268i
$725$	−10.0000	−	17.3205i	−0.371391	−	0.643268i
$726$	7.00000	+	12.1244i	0.259794	+	0.449977i
$727$	−48.0000			−1.78022			−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000			−1.78022			−0.890111	+	0.455744i	$0.849373\pi$
$728$	1.00000	−	3.46410i	0.0370625	−	0.128388i
$729$	13.0000			0.481481
$730$	−1.50000	−	2.59808i	−0.0555175	−	0.0961591i
$731$	1.00000	+	1.73205i	0.0369863	+	0.0640622i
$732$	5.00000	−	8.66025i	0.184805	−	0.320092i
$733$	−51.0000			−1.88373			−0.941864	−	0.335994i	$-0.890928\pi$
$733$	−51.0000			−1.88373			−0.941864	+	0.335994i	$0.890928\pi$
$734$	3.00000	−	5.19615i	0.110732	−	0.191793i
$735$	1.00000	−	1.73205i	0.0368856	−	0.0638877i
$736$	−2.00000			−0.0737210
$737$	−10.0000	+	17.3205i	−0.368355	+	0.638009i
$738$	−3.50000	−	6.06218i	−0.128837	−	0.223152i
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$	7.00000			0.257325
$741$	−28.0000	+	6.92820i	−1.02861	+	0.254514i
$742$	−9.00000			−0.330400
$743$	−8.00000	−	13.8564i	−0.293492	−	0.508342i	0.681141	−	0.732152i	$-0.261484\pi$
$743$	−8.00000	−	13.8564i	−0.293492	−	0.508342i	−0.974633	+	0.223810i	$0.928151\pi$
$744$	−6.00000	−	10.3923i	−0.219971	−	0.381000i
$745$	10.5000	−	18.1865i	0.384690	−	0.666303i
$746$	−19.0000			−0.695639
$747$	−7.00000	+	12.1244i	−0.256117	+	0.443607i
$748$	−1.00000	+	1.73205i	−0.0365636	+	0.0633300i
$749$		0			0
$750$	9.00000	−	15.5885i	0.328634	−	0.569210i
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	0.760263	−	0.649616i	$-0.225070\pi$
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	−0.942715	+	0.333599i	$0.891737\pi$
$752$		0			0
$753$	−40.0000			−1.45768
$754$	5.00000	−	17.3205i	0.182089	−	0.630776i
$755$	8.00000			0.291150
$756$	2.00000	+	3.46410i	0.0727393	+	0.125988i
$757$	−17.0000	−	29.4449i	−0.617876	−	1.07019i	−0.989873	−	0.141958i	$-0.954660\pi$
$757$	−17.0000	−	29.4449i	−0.617876	−	1.07019i	0.371997	−	0.928234i	$-0.378673\pi$
$758$	17.0000	−	29.4449i	0.617468	−	1.06949i
$759$	−8.00000			−0.290382
$760$	−2.00000	+	3.46410i	−0.0725476	+	0.125656i
$761$	7.00000	−	12.1244i	0.253750	−	0.439508i	−0.710805	−	0.703389i	$-0.751669\pi$
$761$	7.00000	−	12.1244i	0.253750	−	0.439508i	0.964555	+	0.263881i	$0.0850027\pi$
$762$	8.00000			0.289809
$763$	1.00000	−	1.73205i	0.0362024	−	0.0627044i
$764$	3.00000	+	5.19615i	0.108536	+	0.187990i
$765$	−0.500000	−	0.866025i	−0.0180775	−	0.0313112i
$766$	18.0000			0.650366
$767$	−6.00000	+	20.7846i	−0.216647	+	0.750489i
$768$	−2.00000			−0.0721688
$769$	7.00000	+	12.1244i	0.252426	+	0.437215i	0.964193	−	0.265200i	$-0.0854381\pi$
$769$	7.00000	+	12.1244i	0.252426	+	0.437215i	−0.711767	+	0.702416i	$0.752105\pi$
$770$	−1.00000	−	1.73205i	−0.0360375	−	0.0624188i
$771$	−15.0000	+	25.9808i	−0.540212	+	0.935674i
$772$	−25.0000			−0.899770
$773$	5.00000	−	8.66025i	0.179838	−	0.311488i	−0.761987	−	0.647592i	$-0.775776\pi$
$773$	5.00000	−	8.66025i	0.179838	−	0.311488i	0.941825	+	0.336104i	$0.109109\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	−24.0000			−0.862105
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$	−7.00000	−	12.1244i	−0.251124	−	0.434959i
$778$	11.5000	+	19.9186i	0.412295	+	0.714116i
$779$	28.0000			1.00320
$780$	7.00000	−	1.73205i	0.250640	−	0.0620174i
$781$	32.0000			1.14505
$782$	1.00000	+	1.73205i	0.0357599	+	0.0619380i
$783$	10.0000	+	17.3205i	0.357371	+	0.618984i
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−11.0000			−0.392607
$786$		0			0
$787$	5.00000	−	8.66025i	0.178231	−	0.308705i	−0.763044	−	0.646347i	$-0.776296\pi$
$787$	5.00000	−	8.66025i	0.178231	−	0.308705i	0.941275	+	0.337642i	$0.109629\pi$
$788$	18.0000			0.641223
$789$	−14.0000	+	24.2487i	−0.498413	+	0.863277i
$790$	−5.00000	−	8.66025i	−0.177892	−	0.308118i
$791$	9.50000	+	16.4545i	0.337781	+	0.585054i
$792$	−2.00000			−0.0710669
$793$	5.00000	−	17.3205i	0.177555	−	0.615069i
$794$	−14.0000			−0.496841
$795$	−9.00000	−	15.5885i	−0.319197	−	0.552866i
$796$	10.0000	+	17.3205i	0.354441	+	0.613909i
$797$	21.0000	−	36.3731i	0.743858	−	1.28840i	−0.206868	−	0.978369i	$-0.566327\pi$
$797$	21.0000	−	36.3731i	0.743858	−	1.28840i	0.950726	−	0.310031i	$-0.100340\pi$
$798$	8.00000			0.283197
$799$		0			0
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$	−6.00000			−0.212000
$802$	11.5000	−	19.9186i	0.406079	−	0.703350i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$	10.0000	+	17.3205i	0.352673	+	0.610847i
$805$	−2.00000			−0.0704907
$806$	−15.0000	−	15.5885i	−0.528352	−	0.549080i
$807$	−36.0000			−1.26726
$808$	−7.50000	−	12.9904i	−0.263849	−	0.457000i
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	0.925312	+	0.379206i	$0.123803\pi$
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	−0.134255	+	0.990947i	$0.542864\pi$
$810$	−5.50000	+	9.52628i	−0.193250	+	0.334719i
$811$	26.0000			0.912983			0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000			0.912983			0.456492	+	0.889728i	$0.349106\pi$
$812$	−2.50000	+	4.33013i	−0.0877328	+	0.151958i
$813$	−30.0000	+	51.9615i	−1.05215	+	1.82237i
$814$	−14.0000			−0.490700
$815$	3.00000	−	5.19615i	0.105085	−	0.182013i
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	−4.00000	−	6.92820i	−0.139942	−	0.242387i
$818$	31.0000			1.08389
$819$	−2.50000	−	2.59808i	−0.0873571	−	0.0907841i
$820$	−7.00000			−0.244451
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	0.607714	−	0.794156i	$-0.292087\pi$
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	−0.991616	+	0.129217i	$0.958754\pi$
$822$	5.00000	+	8.66025i	0.174395	+	0.302061i
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	−0.637419	−	0.770517i	$-0.719998\pi$
$823$	10.0000	−	17.3205i	0.348578	−	0.603755i	0.985997	+	0.166762i	$0.0533313\pi$
$824$	20.0000			0.696733
$825$	−8.00000	+	13.8564i	−0.278524	+	0.482418i
$826$	3.00000	−	5.19615i	0.104383	−	0.180797i
$827$	34.0000			1.18230			0.591148	−	0.806563i	$-0.298675\pi$
$827$	34.0000			1.18230			0.591148	+	0.806563i	$0.298675\pi$
$828$	−1.00000	+	1.73205i	−0.0347524	+	0.0601929i
$829$	13.5000	+	23.3827i	0.468874	+	0.812114i	0.999367	−	0.0355753i	$-0.0113264\pi$
$829$	13.5000	+	23.3827i	0.468874	+	0.812114i	−0.530493	+	0.847690i	$0.677993\pi$
$830$	7.00000	+	12.1244i	0.242974	+	0.420843i
$831$	34.0000			1.17945
$832$	−3.50000	+	0.866025i	−0.121341	+	0.0300240i
$833$	1.00000			0.0346479
$834$	14.0000	+	24.2487i	0.484780	+	0.839664i
$835$	3.00000	+	5.19615i	0.103819	+	0.179820i
$836$	4.00000	−	6.92820i	0.138343	−	0.239617i
$837$	24.0000			0.829561
$838$	−5.00000	+	8.66025i	−0.172722	+	0.299164i
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	−0.950813	−	0.309764i	$-0.899750\pi$
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	0.743670	+	0.668546i	$0.233083\pi$
$840$	−2.00000			−0.0690066
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	9.50000	+	16.4545i	0.327392	+	0.567059i
$843$	−29.0000	−	50.2295i	−0.998813	−	1.72999i
$844$	−14.0000			−0.481900
$845$	11.5000	−	6.06218i	0.395612	−	0.208545i
$846$		0			0
$847$	−3.50000	−	6.06218i	−0.120261	−	0.208299i
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$	−22.0000	+	38.1051i	−0.755038	+	1.30776i
$850$	4.00000			0.137199
$851$	−7.00000	+	12.1244i	−0.239957	+	0.415618i
$852$	16.0000	−	27.7128i	0.548151	−	0.949425i
$853$	25.0000			0.855984			0.427992	−	0.903783i	$-0.359221\pi$
$853$	25.0000			0.855984			0.427992	+	0.903783i	$0.359221\pi$
$854$	−2.50000	+	4.33013i	−0.0855482	+	0.148174i
$855$	2.00000	+	3.46410i	0.0683986	+	0.118470i
$856$		0			0
$857$	−3.00000			−0.102478			−0.0512390	−	0.998686i	$-0.516317\pi$
$857$	−3.00000			−0.102478			−0.0512390	+	0.998686i	$0.516317\pi$
$858$	−14.0000	+	3.46410i	−0.477952	+	0.118262i
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$	1.00000	+	1.73205i	0.0340997	+	0.0590624i
$861$	7.00000	+	12.1244i	0.238559	+	0.413197i
$862$	10.0000	−	17.3205i	0.340601	−	0.589939i
$863$	−18.0000			−0.612727			−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000			−0.612727			−0.306364	+	0.951915i	$0.599112\pi$
$864$	2.00000	−	3.46410i	0.0680414	−	0.117851i
$865$	5.00000	−	8.66025i	0.170005	−	0.294457i
$866$	−9.00000			−0.305832
$867$	−16.0000	+	27.7128i	−0.543388	+	0.941176i
$868$	3.00000	+	5.19615i	0.101827	+	0.176369i
$869$	10.0000	+	17.3205i	0.339227	+	0.587558i
$870$	−10.0000			−0.339032
$871$	25.0000	+	25.9808i	0.847093	+	0.880325i
$872$	−2.00000			−0.0677285
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$	−4.00000	−	6.92820i	−0.135302	−	0.234350i
$875$	−4.50000	+	7.79423i	−0.152128	+	0.263493i
$876$	6.00000			0.202721
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$	5.00000	−	8.66025i	0.168742	−	0.292269i
$879$	14.0000			0.472208
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	−12.5000	−	21.6506i	−0.421136	−	0.729428i	0.574915	−	0.818213i	$-0.305035\pi$
$881$	−12.5000	−	21.6506i	−0.421136	−	0.729428i	−0.996051	+	0.0887846i	$0.971702\pi$
$882$	0.500000	+	0.866025i	0.0168359	+	0.0291606i
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$	2.50000	+	2.59808i	0.0840841	+	0.0873828i
$885$	12.0000			0.403376
$886$	12.0000	+	20.7846i	0.403148	+	0.698273i
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	0.791026	−	0.611783i	$-0.209547\pi$
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	−0.925332	+	0.379157i	$0.876214\pi$
$888$	−7.00000	+	12.1244i	−0.234905	+	0.406867i
$889$	−4.00000			−0.134156
$890$	−3.00000	+	5.19615i	−0.100560	+	0.174175i
$891$	11.0000	−	19.0526i	0.368514	−	0.638285i
$892$	−12.0000			−0.401790
$893$		0			0
$894$	21.0000	+	36.3731i	0.702345	+	1.21650i
$895$		0			0
$896$	1.00000			0.0334077
$897$	−4.00000	+	13.8564i	−0.133556	+	0.462652i
$898$	−30.0000			−1.00111
$899$	15.0000	+	25.9808i	0.500278	+	0.866507i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	4.50000	−	7.79423i	0.149917	−	0.259663i
$902$	14.0000			0.466149
$903$	2.00000	−	3.46410i	0.0665558	−	0.115278i
$904$	9.50000	−	16.4545i	0.315965	−	0.547268i
$905$	−23.0000			−0.764546
$906$	−8.00000	+	13.8564i	−0.265782	+	0.460348i
$907$	21.0000	+	36.3731i	0.697294	+	1.20775i	0.969401	+	0.245481i	$0.0789459\pi$
$907$	21.0000	+	36.3731i	0.697294	+	1.20775i	−0.272108	+	0.962267i	$0.587721\pi$
$908$	−5.00000	−	8.66025i	−0.165931	−	0.287401i
$909$	−15.0000			−0.497519
$910$	−3.50000	+	0.866025i	−0.116024	+	0.0287085i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−4.00000	−	6.92820i	−0.132453	−	0.229416i
$913$	−14.0000	−	24.2487i	−0.463332	−	0.802515i
$914$	−4.50000	+	7.79423i	−0.148847	+	0.257810i
$915$	−10.0000			−0.330590
$916$	1.00000	−	1.73205i	0.0330409	−	0.0572286i
$917$		0			0
$918$	−4.00000			−0.132020
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$	1.00000	+	1.73205i	0.0329690	+	0.0571040i
$921$	−6.00000	−	10.3923i	−0.197707	−	0.342438i
$922$	11.0000			0.362266
$923$	16.0000	−	55.4256i	0.526646	−	1.82436i
$924$	4.00000			0.131590
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$	9.00000	+	15.5885i	0.295758	+	0.512268i
$927$	10.0000	−	17.3205i	0.328443	−	0.568880i
$928$	5.00000			0.164133
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$	−6.00000	+	10.3923i	−0.196748	+	0.340777i
$931$	−4.00000			−0.131095
$932$	−7.00000	+	12.1244i	−0.229293	+	0.397146i
$933$	30.0000	+	51.9615i	0.982156	+	1.70114i
$934$	−1.00000	−	1.73205i	−0.0327210	−	0.0566744i
$935$	2.00000			0.0654070
$936$	−1.00000	+	3.46410i	−0.0326860	+	0.113228i
$937$	9.00000			0.294017			0.147009	−	0.989135i	$-0.453036\pi$
$937$	9.00000			0.294017			0.147009	+	0.989135i	$0.453036\pi$
$938$	−5.00000	−	8.66025i	−0.163256	−	0.282767i
$939$	6.00000	+	10.3923i	0.195803	+	0.339140i
$940$		0			0
$941$	14.0000			0.456387			0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000			0.456387			0.228193	+	0.973616i	$0.426718\pi$
$942$	11.0000	−	19.0526i	0.358399	−	0.620766i
$943$	7.00000	−	12.1244i	0.227951	−	0.394823i
$944$	−6.00000			−0.195283
$945$	2.00000	−	3.46410i	0.0650600	−	0.112687i
$946$	−2.00000	−	3.46410i	−0.0650256	−	0.112628i
$947$	−23.0000	−	39.8372i	−0.747400	−	1.29453i	−0.949065	−	0.315080i	$-0.897969\pi$
$947$	−23.0000	−	39.8372i	−0.747400	−	1.29453i	0.201666	−	0.979454i	$-0.435365\pi$
$948$	20.0000			0.649570
$949$	10.5000	−	2.59808i	0.340844	−	0.0843371i
$950$	−16.0000			−0.519109
$951$	−25.0000	−	43.3013i	−0.810681	−	1.40414i
$952$	−0.500000	−	0.866025i	−0.0162051	−	0.0280680i
$953$	−19.0000	+	32.9090i	−0.615470	+	1.06603i	0.374831	+	0.927093i	$0.377701\pi$
$953$	−19.0000	+	32.9090i	−0.615470	+	1.06603i	−0.990302	+	0.138933i	$0.955633\pi$
$954$	9.00000			0.291386
$955$	3.00000	−	5.19615i	0.0970777	−	0.168144i
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$	20.0000			0.646508
$958$	−3.00000	+	5.19615i	−0.0969256	+	0.167880i
$959$	−2.50000	−	4.33013i	−0.0807292	−	0.139827i
$960$	1.00000	+	1.73205i	0.0322749	+	0.0559017i
$961$	5.00000			0.161290
$962$	−7.00000	+	24.2487i	−0.225689	+	0.781810i
$963$		0			0
$964$	9.50000	+	16.4545i	0.305974	+	0.529963i
$965$	12.5000	+	21.6506i	0.402389	+	0.696959i
$966$	2.00000	−	3.46410i	0.0643489	−	0.111456i
$967$	−42.0000			−1.35063			−0.675314	−	0.737530i	$-0.735992\pi$
$967$	−42.0000			−1.35063			−0.675314	+	0.737530i	$0.735992\pi$
$968$	−3.50000	+	6.06218i	−0.112494	+	0.194846i
$969$	−4.00000	+	6.92820i	−0.128499	+	0.222566i
$970$	−2.00000			−0.0642161
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$	−5.00000	−	8.66025i	−0.160375	−	0.277778i
$973$	−7.00000	−	12.1244i	−0.224410	−	0.388689i
$974$	−32.0000			−1.02535
$975$	20.0000	+	20.7846i	0.640513	+	0.665640i
$976$	5.00000			0.160046
$977$	10.5000	+	18.1865i	0.335925	+	0.581839i	0.983662	−	0.180025i	$-0.0576179\pi$
$977$	10.5000	+	18.1865i	0.335925	+	0.581839i	−0.647737	+	0.761864i	$0.724285\pi$
$978$	6.00000	+	10.3923i	0.191859	+	0.332309i
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$	1.00000			0.0319438
$981$	−1.00000	+	1.73205i	−0.0319275	+	0.0553001i
$982$	8.00000	−	13.8564i	0.255290	−	0.442176i
$983$	8.00000			0.255160			0.127580	−	0.991828i	$-0.459279\pi$
$983$	8.00000			0.255160			0.127580	+	0.991828i	$0.459279\pi$
$984$	7.00000	−	12.1244i	0.223152	−	0.386510i
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$	−2.50000	−	4.33013i	−0.0796162	−	0.137899i
$987$		0			0
$988$	−10.0000	−	10.3923i	−0.318142	−	0.330623i
$989$	−4.00000			−0.127193
$990$	1.00000	+	1.73205i	0.0317821	+	0.0550482i
$991$	−15.0000	−	25.9808i	−0.476491	−	0.825306i	0.523146	−	0.852243i	$-0.324758\pi$
$991$	−15.0000	−	25.9808i	−0.476491	−	0.825306i	−0.999637	+	0.0269367i	$0.991425\pi$
$992$	3.00000	−	5.19615i	0.0952501	−	0.164978i
$993$	36.0000			1.14243
$994$	−8.00000	+	13.8564i	−0.253745	+	0.439499i
$995$	10.0000	−	17.3205i	0.317021	−	0.549097i
$996$	−28.0000			−0.887214
$997$	−12.5000	+	21.6506i	−0.395879	+	0.685682i	−0.993213	−	0.116310i	$-0.962893\pi$
$997$	−12.5000	+	21.6506i	−0.395879	+	0.685682i	0.597334	+	0.801993i	$0.296227\pi$
$998$	−7.00000	−	12.1244i	−0.221581	−	0.383790i
$999$	−14.0000	−	24.2487i	−0.442940	−	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.2.g.d.29.1	✓	2
3.2	odd	2		1638.2.r.e.757.1		2
4.3	odd	2		1456.2.s.b.1121.1		2
7.2	even	3		1274.2.h.d.263.1		2
7.3	odd	6		1274.2.e.c.471.1		2
7.4	even	3		1274.2.e.j.471.1		2
7.5	odd	6		1274.2.h.m.263.1		2
7.6	odd	2		1274.2.g.b.393.1		2
13.2	odd	12		2366.2.d.c.337.2		2
13.3	even	3		2366.2.a.b.1.1		1
13.9	even	3	inner	182.2.g.d.113.1	yes	2
13.10	even	6		2366.2.a.i.1.1		1
13.11	odd	12		2366.2.d.c.337.1		2
39.35	odd	6		1638.2.r.e.1387.1		2
52.35	odd	6		1456.2.s.b.113.1		2
91.9	even	3		1274.2.e.j.165.1		2
91.48	odd	6		1274.2.g.b.295.1		2
91.61	odd	6		1274.2.e.c.165.1		2
91.74	even	3		1274.2.h.d.373.1		2
91.87	odd	6		1274.2.h.m.373.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.g.d.29.1	✓	2	1.1	even	1	trivial
182.2.g.d.113.1	yes	2	13.9	even	3	inner
1274.2.e.c.165.1		2	91.61	odd	6
1274.2.e.c.471.1		2	7.3	odd	6
1274.2.e.j.165.1		2	91.9	even	3
1274.2.e.j.471.1		2	7.4	even	3
1274.2.g.b.295.1		2	91.48	odd	6
1274.2.g.b.393.1		2	7.6	odd	2
1274.2.h.d.263.1		2	7.2	even	3
1274.2.h.d.373.1		2	91.74	even	3
1274.2.h.m.263.1		2	7.5	odd	6
1274.2.h.m.373.1		2	91.87	odd	6
1456.2.s.b.113.1		2	52.35	odd	6
1456.2.s.b.1121.1		2	4.3	odd	2
1638.2.r.e.757.1		2	3.2	odd	2
1638.2.r.e.1387.1		2	39.35	odd	6
2366.2.a.b.1.1		1	13.3	even	3
2366.2.a.i.1.1		1	13.10	even	6
2366.2.d.c.337.1		2	13.11	odd	12
2366.2.d.c.337.2		2	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 + 1.73205i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} -2.00000 q^{12} +(-3.50000 + 0.866025i) q^{13} +1.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} -1.00000 q^{18} +(2.00000 - 3.46410i) q^{19} +(-0.500000 + 0.866025i) q^{20} +2.00000 q^{21} +(1.00000 - 1.73205i) q^{22} +(-1.00000 - 1.73205i) q^{23} +(-1.00000 - 1.73205i) q^{24} -4.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} +4.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(2.50000 + 4.33013i) q^{29} +(-1.00000 + 1.73205i) q^{30} +6.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} -1.00000 q^{34} +(0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +4.00000 q^{38} +(-5.00000 - 5.19615i) q^{39} -1.00000 q^{40} +(3.50000 + 6.06218i) q^{41} +(1.00000 + 1.73205i) q^{42} +(1.00000 - 1.73205i) q^{43} +2.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(1.00000 - 1.73205i) q^{46} +(1.00000 - 1.73205i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} -2.00000 q^{51} +(1.00000 - 3.46410i) q^{52} -9.00000 q^{53} +(2.00000 + 3.46410i) q^{54} +(-1.00000 - 1.73205i) q^{55} +(-0.500000 + 0.866025i) q^{56} +8.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(3.00000 - 5.19615i) q^{59} -2.00000 q^{60} +(-2.50000 + 4.33013i) q^{61} +(3.00000 + 5.19615i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(-3.50000 + 0.866025i) q^{65} +4.00000 q^{66} +(-5.00000 - 8.66025i) q^{67} +(-0.500000 - 0.866025i) q^{68} +(2.00000 - 3.46410i) q^{69} +1.00000 q^{70} +(-8.00000 + 13.8564i) q^{71} +(0.500000 - 0.866025i) q^{72} -3.00000 q^{73} +(3.50000 - 6.06218i) q^{74} +(-4.00000 - 6.92820i) q^{75} +(2.00000 + 3.46410i) q^{76} -2.00000 q^{77} +(2.00000 - 6.92820i) q^{78} -10.0000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-3.50000 + 6.06218i) q^{82} +14.0000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(-0.500000 + 0.866025i) q^{85} +2.00000 q^{86} +(-5.00000 + 8.66025i) q^{87} +(1.00000 + 1.73205i) q^{88} +(3.00000 + 5.19615i) q^{89} -1.00000 q^{90} +(-1.00000 + 3.46410i) q^{91} +2.00000 q^{92} +(6.00000 + 10.3923i) q^{93} +(2.00000 - 3.46410i) q^{95} +2.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(0.500000 - 0.866025i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9} + q^{10} - 2 q^{11} - 4 q^{12} - 7 q^{13} + 2 q^{14} + 2 q^{15} - q^{16} - q^{17} - 2 q^{18} + 4 q^{19} - q^{20} + 4 q^{21}+ \cdots + 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 + 2 * q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9 + q^10 - 2 * q^11 - 4 * q^12 - 7 * q^13 + 2 * q^14 + 2 * q^15 - q^16 - q^17 - 2 * q^18 + 4 * q^19 - q^20 + 4 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 - 8 * q^25 - 5 * q^26 + 8 * q^27 + q^28 + 5 * q^29 - 2 * q^30 + 12 * q^31 + q^32 + 4 * q^33 - 2 * q^34 + q^35 - q^36 - 7 * q^37 + 8 * q^38 - 10 * q^39 - 2 * q^40 + 7 * q^41 + 2 * q^42 + 2 * q^43 + 4 * q^44 - q^45 + 2 * q^46 + 2 * q^48 - q^49 - 4 * q^50 - 4 * q^51 + 2 * q^52 - 18 * q^53 + 4 * q^54 - 2 * q^55 - q^56 + 16 * q^57 - 5 * q^58 + 6 * q^59 - 4 * q^60 - 5 * q^61 + 6 * q^62 + q^63 + 2 * q^64 - 7 * q^65 + 8 * q^66 - 10 * q^67 - q^68 + 4 * q^69 + 2 * q^70 - 16 * q^71 + q^72 - 6 * q^73 + 7 * q^74 - 8 * q^75 + 4 * q^76 - 4 * q^77 + 4 * q^78 - 20 * q^79 - q^80 + 11 * q^81 - 7 * q^82 + 28 * q^83 - 2 * q^84 - q^85 + 4 * q^86 - 10 * q^87 + 2 * q^88 + 6 * q^89 - 2 * q^90 - 2 * q^91 + 4 * q^92 + 12 * q^93 + 4 * q^95 + 4 * q^96 - 2 * q^97 + q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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